Again by the inequality in [1]}, we have
\(N(\epsilon ,[0,1],\tilde{\rho })\le N\left(\left(C^{-1}\epsilon \sqrt{n/\tilde{\kappa }_{kk}\hat{\kappa }_{k+1,k+1}}\right)^{2},[0,1],|\cdot |\right)\lesssim \frac{1}{(\epsilon \sqrt{n/\tilde{\kappa }_{kk}\hat{\kappa }_{k+1,k+1}})^{2}}.\) 
